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The rectified order-5 hexagonal tiling honeycomb, t 1 {6,3,5}, has icosahedron and trihexagonal tiling facets, with a pentagonal prism vertex figure. It is similar to the 2D hyperbolic infinite-order square tiling, r{∞,5} with pentagon and apeirogonal faces. All vertices are on the ideal surface.
In geometry, the truncated order-5 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t 0,1 {6,5}. Related polyhedra and tiling
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane.There are 2 dodecagons (12-sides) and one triangle on each vertex.. As the name implies this tiling is constructed by a truncation operation applied to a hexagonal tiling, leaving dodecagons in place of the original hexagons, and new triangles at the original vertex locations.
The order-5 truncated pentagonal hexecontahedron is a convex polyhedron with 72 faces: 60 hexagons and 12 pentagons triangular, with 210 edges, and 140 vertices. Its dual is the pentakis snub dodecahedron. It is Goldberg polyhedron {5+,3} 2,1 in the icosahedral family, with chiral symmetry. The relationship between pentagons steps into 2 ...
In geometry, the order-5 hexagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {6,5}. Related polyhedra and tiling.
For example, in a polyhedron (3 ... Order-5 hexagonal tiling honeycomb; Order-6 hexagonal tiling honeycomb; ... Truncated 5-demicube, Cantellated 5-demicube, ...
The truncated order-5 cubic honeycomb, , has truncated cube and icosahedron cells, with a pentagonal pyramid vertex figure. It can be seen as analogous to the 2D hyperbolic truncated order-5 square tiling , t{4,5}, with truncated square and pentagonal faces:
With a final vertex 3 4.6, 4 more contiguous equilateral triangles and a single regular hexagon. However, this notation has two main problems related to ambiguous conformation and uniqueness [ 2 ] First, when it comes to k-uniform tilings, the notation does not explain the relationships between the vertices.